The origin of the energy provided by hydrothermal vents is the internal heat of the planet.
The reduced substances, like elemental hydrogen and hydrogen sulfide, are produced by the oxidation of the iron(II) ions from volcanic rocks, which is converted by water into rust.
The volcanic rocks contain this more reduced form of iron, because they come from higher temperatures, where their constituent minerals are in chemical equilibrium. When the volcanic rocks reach ambient temperature, the volcanic rocks are no longer in chemical equilibrium with water. This source of chemical energy powers the hydrothermal vents and the associated life.
So the conditions for the appearance of life are an internal source of heat in the planet or satellite and some form of volcanism that can bring substances from the hot deep interior to the cold surface.